In the related art, an NOx occlusion reduction type catalyst is known as a catalyst which reduces and purifies a nitrogen compound (NOx) in an exhaust gas discharged from an internal combustion engine. When the exhaust gas is under a lean atmosphere, the NOx occlusion reduction type catalyst occludes the NOx contained in the exhaust gas. When the exhaust gas is under a rich atmosphere, the NOx occlusion reduction type catalyst detoxifies the occluded NOx through reducing and purifying by hydrocarbon contained in the exhaust gas, and discharges the NOx. For this reason, in a case where the NOx occlusion amount of the catalyst reaches a predetermined amount, in order to recover NOx occlusion capacity, it is necessary to regularly perform a so-called NOx purge which makes the exhaust gas be in a rich state by a post injection or an exhaust pipe injection (for example, see JP-A-2008-202425).
In the NOx occlusion reduction type catalyst, a sulfur oxide contained in the exhaust gas (hereinafter, referred to as SOx) is also occluded. When the SOx occlusion amount increases, the NOx purification capacity of the NOx occlusion reduction type catalyst is reduced, which is problematic. For this reason, in a case where an SOx occlusion amount reaches a predetermined amount, in order that the SOx is desorbed from the NOx occlusion reduction type catalyst to recover the NOx occlusion reduction type catalyst from S-poisoning, it is necessary to regularly perform the so-called SOx purge in which an unburned fuel is supplied to an upstream-side oxidation catalyst by the post injection or the exhaust pipe injection to raise an exhaust temperature to an SOx desorption temperature (for example, see JP-A-2009-047086).